Abstract
The isothermal method is used to derive an expression for the static conductivity of electrons in an external field, under ergodic conditions, following Kubo's paper. After appropriate approximations, a formula is obtained which reduces to the usual Boltzmann expression in the weak-coupling limit and which is used to analyse the three-dimensional Anderson transition and the one-dimensional conductivity of non-interacting electrons. If states have a finite extension right up to the three-dimensional mobility edge εc, the conductivity as a function of energy ε is found to vary as (ε—εc )v(d-2+η) for ε ≥ εc (d = 3) with ν = ⅗ and η =⅓ If they are extended, a minimum metallic conductivity follows. However, the method does not predict the nature of the states.